Transient Pressure Response of a Well With Partial Completion in a Two-Layer Crossflowing Reservoir

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ABSTRACT Although the technical literature contains several transient pressure response models for reservoirs producing multiple crossflowing layers, none of these models is adequate for the applications where they are most needed. None of these models accounts for partial completion. Further, all but one of these models approximate the crossflow through a steady-state assumption and ignore the variation of the pressure within each layer in the vertical direction. Layered models with crossflow are often used to interpret tests in thick carbonate reservoirs or in wells with bot-tomwater drive or gas caps. Partial completion, often in the extreme form, is invariably employed in such systems. Ignoring it in test interpretation may lead to incorrect estimation of some key parameters and unidentifiability of others. An analytic model is presented for the transient pressure response of such systems. This model rigorously accounts for both partial completion and the dynamics of vertical flow. The Laplace domain solution includes a different skin factor in each layer and can account for the effects of wellbore storage and dual porosities. The solution is obtained by applying the finite Hankel transforms and employing the pressure averaging technique. Computer-based symbolic manipulation was necessary to render the solution into a form suitable for practical evaluation. The new model enables improved interpretation of well tests in several types of reservoirs to yield parameters that cannot be estimated with the existing models (e.g., the vertical permeabilities in two communicating layers, and. the horizontal mobility in the gas cap or in the water zone communicating with an oil reservoir). This model can also be used for interpretation of the single well vertical interference test.